A079983 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,1,2}.

1, 1, 1, 1, 3, 6, 12, 20, 35, 60, 114, 207, 375, 671, 1213, 2180, 3954, 7139, 12892, 23250, 41996, 75793, 136891, 247133, 446211, 805505, 1454390, 2625744, 4740788, 8559108, 15453182, 27899503, 50371415, 90942627, 164192549, 296440115

Offset

0,5

Comments

Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,-1,2}.

References

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Links

Table of n, a(n) for n=0..35.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

Formula

a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-5) +4*a(n-6) -4*a(n-7) -3*a(n-8) -3*a(n-9) +3*a(n-10) +3*a(n-11) -5*a(n-12) +4*a(n-13) +4*a(n-14) +a(n-15) -2*a(n-16) -a(n-17) +a(n-18) -a(n-19) -a(n-20)

G.f.: -(x^2-1)*(x^12+2*x^9-x^6-2*x^3+1)/(x^20 +x^19 -x^18 +x^17 +2*x^16 -x^15 -4*x^14 -4*x^13 +5*x^12 -3*x^11 -3*x^10 +3*x^9 +3*x^8 +4*x^7 -4*x^6 +x^5 -x^3 -x^2 -x+1)

Crossrefs

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.

Sequence in context: A320613 A006128 A247661 * A028926 A038577 A028925

Adjacent sequences: A079980 A079981 A079982 * A079984 A079985 A079986

Keyword

nonn

Author

Vladimir Baltic, Feb 17 2003

Status

approved